A102616
Nonprime numbers of order 3.
Original entry on oeis.org
1, 14, 16, 22, 24, 25, 30, 33, 35, 36, 39, 44, 46, 48, 50, 51, 54, 55, 56, 62, 64, 66, 68, 69, 70, 75, 76, 77, 80, 85, 86, 87, 90, 92, 93, 94, 96, 100, 102, 104, 105, 108, 111, 115, 116, 117, 118, 120, 122, 123, 124, 126, 130, 132, 134, 136, 138, 142, 144, 145, 148, 150
Offset: 1
Nonprime(2) = 4.
Nonprime(4) = 8.
Nonprime(8) = 14, the 2nd entry.
Let A = primes
A000040, B = nonprimes
A018252. The 2-level compounds are AA =
A006450, AB =
A007821, BA =
A078782, BB =
A102615. The 3-level compounds AAA, AAB, ..., BBB are
A038580,
A049078,
A270792,
A102617,
A270794,
A270796,
A102216.
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# For Maple code for the prime/nonprime compound sequences (listed in cross-references) see A003622. - N. J. A. Sloane, Mar 30 2016
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nonPrime[n_] := FixedPoint[n + PrimePi[ # ] &, n]; Nest[ nonPrime, Range[62], 3] (* Robert G. Wilson v, Feb 04 2005 *)
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\\ We perform nesting(s) with a loop.
cics(n,m) = { local(x,y,z); for(x=1,n, z=x; for(y=1,m+1, z=nonprime(z); ); print1(z",") ) }
nonprime(n) = { local(c,x); c=1; x=0; while(c <= n, x++; if(!isprime(x),c++); ); return(x) }
A270795
The prime/nonprime compound sequence BAB.
Original entry on oeis.org
4, 12, 21, 28, 34, 42, 52, 60, 65, 74, 84, 95, 98, 106, 119, 128, 133, 135, 141, 147, 170, 177, 180, 192, 195, 209, 214, 220, 231, 246, 250, 253, 284, 288, 290, 295, 301, 316, 323, 329, 336, 339, 351, 365, 382, 387, 390, 394, 417, 429, 432, 445, 462, 470, 474, 481, 490, 505, 516, 518, 532, 538, 543, 550, 559, 566
Offset: 1
Let A = primes
A000040, B = nonprimes
A018252. The 2-level compounds are AA =
A006450, AB =
A007821, BA =
A078782, BB =
A102615. The 3-level compounds AAA, AAB, ..., BBB are
A038580,
A049078,
A270792,
A102617,
A270794,
A270796,
A102216.
Original entry on oeis.org
1, 2, 7, 13, 14, 21, 25, 26, 31, 37, 41, 42, 49, 50, 55, 61, 62, 69, 73, 74, 81, 82, 87, 93, 97, 98, 103, 109, 110, 117, 121, 122, 127, 133, 137, 138, 145, 146, 151, 157, 161, 162, 167, 173, 174, 181, 185, 186, 193, 194, 199, 205, 206, 213, 217, 218, 223, 229, 233, 234, 241, 242, 247, 253
Offset: 1
The first odious number, A000069(1) = 1, and A000069(1) = 1, so a(1) = 1.
The second odious number, A000069(2) = 2, and A000069(2) = 2, so a(2) = 2.
Those were the only fixed points of A000069, and after that, we have:
The third odious number, A000069(3) = 4, and A000069(4) = 7, thus a(3) = 7.
The fourth odious number, A000069(4) = 7, and A000069(7) = 13, thus a(4) = 13.
A004119 from term 7 onward is a subsequence.
A175250
Nonprimes (A018252) with noncomposite (A008578) subscripts.
Original entry on oeis.org
1, 4, 6, 9, 12, 18, 21, 26, 28, 34, 42, 45, 52, 57, 60, 65, 74, 81, 84, 91, 95, 98, 106, 112, 119, 128, 133, 135, 141, 143
Offset: 1
a(5) = 12 because a(5) = b(q(5)) = b(7) = 12, q = noncomposite, b = nonprime.
A161186
In the sequence of nonprime numbers, an element k's position is either prime or nonprime. If k's position is prime, f(k)= the k-th nonprime-positioned element, else f(k) is the k-th prime-positioned element. Iterated application of x-> f(x) gives disjoint sequences generated by the first elements, which form the current sequence.
Original entry on oeis.org
1, 6, 8, 9, 10, 12, 15, 18, 20, 21, 22, 25, 26, 27, 32, 33, 34, 35, 36, 38, 40, 44, 45, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 64, 66, 69, 70, 72, 75, 76, 77, 78, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 98, 99, 100, 102, 104, 108, 110, 112, 114, 115, 116, 117, 120
Offset: 1
The nonprime numbers are: [1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20].
Those with prime positions are: [4, 6, 9, 12, 18].
Those with nonprime positions are: [1, 8, 10, 14, 15, 16, 20].
So we have {f(1)} = {1,4,14,60,...}, {f(6)} = {6,16,74,...}, {f(8)} ={8,28,56,...}; so the current sequence are the first elements, {1,6,8,...etc}.
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lista(nn) = {my(va = select(x->(! isprime(x)), [1..nn])); my(vap = vector(primepi(#va), k, va[prime(k)])); my(vanp = Vec(setminus(va, vap))); my(vused = vector(#va), ok=1, last=0, list=List(), new, ok2); while(ok, last++; while ((last <= #vused) && vused[last], last++); if (last > #vused, break); new = va[last]; listput(list, new); ok2 = 1; my(list1 = List()); listput(list1, new); while(ok2, pos = setsearch(va, new); if (!pos, ok2=0, vused[pos] = 1; if (isprime(pos), if (new <= #vanp, new = vanp[new], ok2=0), if (new <= #vap, new = vap[new], ok2=0);); listput(list1, new);););); Vec(list);} \\ Michel Marcus, Aug 18 2022
A175248
Noncomposites (A008578) with noncomposite (A008578) subscripts.
Original entry on oeis.org
1, 2, 3, 7, 13, 29, 37, 53, 61, 79, 107, 113, 151, 173, 181, 199, 239, 271, 281, 317, 349, 359, 397, 421, 457, 503, 541, 557, 577, 593, 613, 701, 733, 769, 787, 857, 863, 911, 953, 983, 1021, 1061, 1069, 1151, 1163, 1193, 1213, 1291, 1399, 1429, 1439, 1459
Offset: 1
a(5) = 13 because a(5) = q(q(5)) = q(7) = 13, q = noncomposite.
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